The properties of the quantum supergroup $G{L}_{p,q}(1|1)$

Abstract

In this paper properties of the quantum supermatrices in the quantum supergroup $G{L}_{p,q}(1|1)$ are discussed. It is shown that any element of $G{L}_{p,q}(1|1)$ can be expressed as the exponential of a matrix of non-commuting elements, like the group $G{L}_q(1|1)$. An explicit construction of this exponential representation is presented.

12 pages